The Boundedness Of Commutators Of Two Kinds Of Integral Operators

In the recent paper, we study the boundedness of commutators of two kinds of integral oper-ators. The paper is constituted with four thesis.In chapter1, we introduce the background and main results about the Toeplitz operator related to singular integral operator and other operators associated with it. Besides, we also simply illustrate how and why this topics comes out.In chapter2. we present A-center BMO estimates for the Toeplitz operator related to singular integral operator with non-smooth kernels. The commutators is (?)ba.In chapter3, we discuss the boundedness of Toeplitz operator related to singular integral operator on the λ-center morrey spaces and Hardy spaces. The commutators is TbIn chapter4, we consider the Sharp weight norm inequality for the commutator of maximal fractional integral operators. The commutators is Mb,αm.